Rate of convergence for asymptotic variance of the Horvitz-Thompson estimator
Rate of convergence for asymptotic variance of the Horvitz-Thompson estimator
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DOI：
10.1016/s0378-3758(98)00107-4
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发表时间：
1998-10-01
影响因子：
0.9
通讯作者：
Berger, YG
中科院分区：
文献类型：
--
作者：
Berger, YG
在没有放回和不等概率的情况下从总体中绘制不同的单位是文献中经常考虑的问题（例如 Hanif 和 Brewer, 1980, Int. Statist. Rev. 48, 317-355）。在这种情况下，样本平均值是总体平均值的有偏估计。因此，我们使用无偏 Horvitz-Thompson 估计器 (1951)。在这项工作中，我们将注意力集中在该估计量的方差上。方差计算起来很麻烦，因为它需要计算大量的二阶包含概率。使用不需要大量计算的近似值会很有帮助。 Hajek (1964) 方差近似提供了这一优势，因为它不受二阶包含概率的影响。 Hajek（1964）证明，这种近似在实际中通常无法满足的限制条件下是有效的。在本文中，我们给出了更一般的条件，并且表明这种近似对于大多数实际问题来说仍然是可以接受的。 (C) 1998 Elsevier Science B.V. 保留所有权利。
Drawing distinct units without replacement and with unequal probabilities from a population is a problem often considered in the literature (e.g. Hanif and Brewer, 1980, Int. Statist. Rev. 48, 317-355). In such a case, the sample mean is a biased estimator of the population mean. For this reason, we use the unbiased Horvitz-Thompson estimator (1951). In this work, we focus our interest on the variance of this estimator. The variance is cumbersome to compute because it requires the calculation of a large number of second-order inclusion probabilities. It would be helpful to use an approximation that does not need heavy calculations. The Hajek (1964) variance approximation provides this advantage as it is free of second-order inclusion probabilities. Hajek (1964) proved that this approximation is valid under restrictive conditions that are usually not fulfilled in practice. In this paper, we give more general conditions and we show that this approximation remains acceptable for most practical problems. (C) 1998 Elsevier Science B.V. All rights reserved.